X169

X85-CEVA CONJUGATE OF X1

X169 = X85-Ceva conjugate of X1
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 4, 9 }: Orthocenter–Spieker Line { 1, 41 }: Central Line L(1, 41) { 65, 218 }: Central Line L(65, 218) { 57, 277 }: Central Line L(57, 277) { 63, 379 }: Central Line L(63, 379) { 46, 672 }: Central Line L(46, 672) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_85 = ISOTOMIC CONJUGATE OF X(9) (0.5610, 0.2421) X_1 = INCENTER (0.5714, 0.2333) X_4 = ORTHOCENTER (0.6122, 0.3958) X_9 = MITTENPUNKT (0.5110, 0.1615) X_41 = -CEVA CONJUGATE OF X(31) (0.5823, 0.2244) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_218 = -CEVA CONJUGATE OF X(55) (0.6557, 0.3333) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_277 = ISOGONAL CONJUGATE OF X(218) (0.4242, 0.1335) X_63 = ISOGONAL CONJUGATE OF X(19) (0.4566, 0.0823) X_379 = EULER LINE INTERCEPT OF LINE X(6)X(7) (0.5733, 0.2937) X_46 = -CEVA CONJUGATE OF X(1) (0.6917, 0.4543) X_672 = CROSSDIFFERENCE OF X(1) AND X(514) (1.9245, 2.2184) X_169 = -CEVA CONJUGATE OF X(1) (0.5497, 0.2510) A B C X85 X1 X4 X9 X41 X65 X218 X57 X277 X63 X379 X46 X672 X169 (a, b, c) = (5, 6, 7) | AB = 1

X169 (X85-CEVA CONJUGATE OF X1) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(- (\sin A)\cos^{2}(A/2) + (\sin B)\cos^{2}(B/2) + (\sin C)\cos^{2}(C/2) : :\)
Search Value (6, 9, 13): \(1.504667690499\)
▸ Alternate Coordinates1 form

  • Trilinears: \(a^{3} - a^{2} (b + c) + a (b^{2} + c^{2}) - (b - c)^{2} (b + c) : :\)

▸ Incident Central Lines10 lines

{1, 41}, {3, 910}, {4, 9}, {6, 942}, {46, 672}, {57, 277}, {63, 379}, {65, 218}, {220, 517}, {572, 610}

▸ Functional Relations5 relations